what angular velocity would produce an "artificial gravity" of 9.80 m/s at the rim?

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Chapter10: Fixed-axis Rotation
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Problem 48P: An ultracentrifuge accelerates from to 100,000 rpm in 2.00 min. (a) What is the average angular...
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A rotating space station is said to create "artificial gravity"-a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and
bone strength more naturally than in non-rotating space environments. If the space station is 160 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s at the rim?
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Transcribed Image Text:A rotating space station is said to create "artificial gravity"-a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 160 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s at the rim? rpm
Expert Solution
Step 1 centripetal acceleration

 When an object moves in a circular path it experience an acceleration having magnitude  equals square of linear velocity divided by radius of circular path and it points towards the center of the circular path. 

    Mathematically, centripetal acceleration, 

                   a= v2/ r    ....... .... 1

      Where v is linear velocity and r is radius of circular path. 

 The linear velocity and angular velocity are related as, 

                 v = rω    ............. . 2

   Where  is angular velocity. 

 

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